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Particle / Anti-particle Annihilations

  1. Mar 23, 2005 #1
    Are there any experimental or theoretical limits on the distance at which a particle / anti-particle pair ( or pair for short ) can annihilate? If there is, are there any limits on the duration a pair must be within said distance in order for an annihilation to occur?

    In other words: Do there exist, at the very least theoretical, conditions under which a colocated ( read: very close ) pair can be guaranteed to seperate fast enough to "escape annihilation" ?

    I realize this question relies on a great deal more than the simple notions of distance, time and motion, so any reference material would be greatly appreciated.


    -joeboo
     
  2. jcsd
  3. Mar 23, 2005 #2

    jtbell

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    Staff: Mentor

    At the quantum-mechanical level, physicists don't think in terms of distance of closest approach, because you can't think of either particle as having a definite position at any particular time. (Remember the Heisenberg Uncertainty Principle?)

    Instead, we think in probabilistic terms, using a quantity called the interaction cross section. If we have a thin target of thickness [itex]dx[/itex], containing [itex]n[/itex] electrons per m^3, and we fire [itex]N_0[/itex] positrons at it, the number [itex]dN[/itex] that annihilate is, on the average,

    [tex]dN = \sigma N_0 n dx[/tex]

    where the proportionality constant [itex]\sigma[/itex] is the interaction cross section for annihilation. We can measure [itex]\sigma[/itex] by counting how many positrons actually annihilate, and calculating

    [tex] \sigma = \frac {1}{N_0 n} \frac {dN}{dx}[/tex]

    We can also predict [itex]\sigma[/itex] from theory, using quantum electrodynamics. It depends on the energy of the positrons.

    A Google search on

    electron positron annihilation cross section

    turns up a lot of pages, some of which have theoretically-derived formulas for [itex]\sigma[/itex], and others which have the measured values.
     
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